The United States has told Syrian rebel factions they should not expect military support to help resist a Russian-backed government offensive to regain opposition-held parts of Syria, bordering Jordan and the Israeli-occupied Golan Heights.

A copy of a message sent by Washington to the heads of Free Syrian Army (FSA) groups said the US government wanted to make clear that "you should not base your decisions on the assumption or expectation of a military intervention by us".

'The letter's contents mean that American will not be able to help the south - in other words, they are saying you're on your own'

- Opposition commander in southern Syria

The US warning came as the Syrian army, backed by the Russian Air Force, repelled a rebel attack killing around 70 fighters, according to the Russian new agencies that cited the Russian Defence Ministry on Monday.

According to the Syrian Observatory for Human Rights, five civilians including two women were killed on Sunday after Russian strikes on Al-Hirak, Al-Sura and Alma, three rebel-held towns in the southwest province of Daraa.

Two hospitals were also damaged in the attacks, forcing medical staff to shut them down temporarily, according to the monitor.

Key parts of southern Syria fall under a "de-escalation zone" agreed by Russia, the US and Jordan last July. Since the agreement, Moscow's air force - active in Syria since 2015 - had refrained from bombing the south.

But late on Saturday, Russian jets started to provide air cover for the expanding Syrian army offensive striking Daraa city, also under rebel control. Early on Sunday at least 20 raids struck Basra al-Harir, a town east of the city.

"We don't care if it's Russian air cover or not. We are on the ground and steadfast," said Abu Ayham, a field commander with Ahrar al-Ashaer rebel group.

Rebels have returned fire into government territory, killing a girl in the Sweida province and wounding three people in the provincial capital of the same name on Sunday, state news agency SANA said.

Escalating bombardment has displaced around 17,000 people from rebel-held towns in Daraa's eastern countryside, according to the Observatory.

'You're on your own'

Over the course of Syria's seven-year war, the US has supported the FSA with millions of dollars worth of arms and paid monthly salaries to thousands of rebels under a military aid programme run by the Central Intelligence Agency.

Ahead of the southern offensive, the US warned Syrian President Bashar al-Assad and his Russian allies that violations of a "de-escalation" zone agreed by the US and Russia last year would have "serious repercussions" and pledged "firm and appropriate measures".

The toughly worded statement raised the hopes of the Western-backed opposition of a possible American military intervention in the event that the Syrian army's bombing campaign broadens to an all-out offensive across the southwest.

Daraa province residents who recently fled the government offensive at the border with the Israeli-occupied Golan Heights (AFP)

But analysts believe the aid has dropped after US President Donald Trump decided last year to shut down the programme and the US message to the rebels has made it clear that they can't rely on American backing.

One opposition commander in the south who received the US warning said: "The letter's contents mean that America will not be able to help the south - in other words, they are saying 'you're on your own'."

Over the weekend residents cited intense air reconnaissance by jets believed to be Russian, flying at high altitudes over Daraa city where rebels control a portion of the provincial capital along the Jordanian border.

Syrian state media said rebels had fired indiscriminately on residential areas of the city causing several casualties, adding that the army had hit what it called "terrorist" hideouts.

Since the start of the offensive last week, the Syrian government has mostly deployed artillery and rockets. Russian warplanes that were critical to the recapture of other rebel-held areas were conspicuously absent.

Throwing in Russia's full military weight in the campaign to regain southern Syria will weaken the ability of rebel groups to hold their ground.

The southwest is of strategic concern to US ally Israel, which this year stepped up attacks on Iran-backed militia allied to Assad.

US ally Jordan, which has been worried by the escalation, said it was engaged in intensive diplomacy with Washington and Moscow to preserve the zone and prevent a wider confrontation.

The loss of opposition-held southern Syria would deal a major blow to the rebel cause. It could secure the reopening of a major international border crossing with Jordan.

Daraa city is seen by the opposition as the cradle of the 2011 uprising that began as a peaceful protest movement against Assad's authoritarian rule but has spread across the country and degenerated into civil war.